Boris Johnson has suggested Theresa May promised to give the NHS an extra £350m a week at the launch of the Conservative party manifesto, when neither she nor the document made any such promise.

The foreign secretary was pressed on why there was no pledge from the Tories to use any proceeds from Brexit to fund the NHS, when handing over £350m a week was a flagship promise of his campaign to leave the European Union.

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Asked on ITV’s Peston on Sunday why the sum was not in the manifesto, Johnson said: “It is. It is. Theresa May, she said it at the launch of the manifesto … She said we are going to take back control.”

ITV News’ political editor, Robert Peston, said: “Where?”, but Johnson went straight into a speech about how the election was a contest between May and Jeremy Corbyn as leaders.

At the manifesto launch, May made a promise to “take back control of [EU] structural funds and use them to strengthen our union and reduce inequalities between our communities”.

However, there was no mention of any of this money specifically going to the NHS.

A senior Conservative source said Johnson was saying a commitment to take money back from the EU and spend it on services such as the NHS was in the manifesto but he had been cut off several times by the interviewer.

Since the referendum, she and her cabinet ministers have repeatedly been challenged about why they are not honouring the pledge that was emblazoned on a bus used to transport Johnson on the campaign trail.

The former leave strategist Dominic Cummings has suggested it was instrumental in helping the leave campaign win the contest.

Vote Leave Watch, a group pressing for the pledge to be honoured, has accused Johnson of “taking the public for fools”.

The foreign secretary was also caught sneaking a look at Peston’s questions before their Sunday morning TV encounter. Peston later tweeted a series of pictures showing Johnson rifling through his notes while he was questioning other guests.

In the interview with ITV, Johnson was also pressed about reducing immigration, another key promise of the leave campaign. He said this would happen “when we take back control” from the EU and backed May’s target of getting numbers down to the tens of thousands rather than hundreds of thousands a year.

Separately, Corbyn, the Labour leader, said that if he gained power he would put in place a migration policy based on the needs of society.

He added immigration would “probably be lower” but he did not want to make predictions. “Freedom of movement obviously ends when you leave the European Union because it’s a condition of the membership,” he told Sky News’s Sophy Ridge On Sunday.

He added: “I want there to be fair immigration based on the needs of our society. That is the proper way of approaching it.”

Pressed further on the issue, Corbyn went on: “I want us to have a society that works and I cannot get into a numbers game because I don’t think it works.”

In a trickier section of the interview, the Labour leader was repeatedly asked to condemn the IRA, following a fresh string of newspaper stories about his links to figures in the militant group in the 1980s. He said: “Bombing is wrong, of course all bombing is wrong and of course I condemn it … I think what you have to say is all bombing has to be condemned and you have to bring about a peace process.

“In the 1980s Britain was looking for a military solution in Ireland. It clearly was never going to work. Ask anyone in the British army at that time.

“Therefore you have to seek a peace process. You condemn the violence of those that laid bombs that killed large of numbers of innocent people and I do.”

Asked to condemn the IRA without equating it to the deaths caused by British security services, Corbyn said: “And there were loyalist bombs as well, which you haven’t mentioned. I condemn all the bombing by the both loyalists and the IRA.”

In another Sky interview, Tim Farron, the Lib Dem leader, also came under pressure in a interview over his views on abortion, which he described in an interview 10 years ago as morally wrong.

Asked five times whether he still believed it was wrong, Farron stressed he believed women should have access to abortion which is “legal and safe”.

Told by Ridge he had not been clear on the question of morality, he replied: “Well, I believe women should have access under law which is safe and legal, and I think that’s the critical issue - do you believe people should be able to make that choice under law, and do you believe the law as it stands is right and the science that dictates, or rather underlines, that law is right. I do believe that, I did then and I do now.”